पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

190 PAÑCASIDDHĀNTIKĀ VIII.14 Parallax correction and orbital diameter 13. Multiply the true daily motion of the Moon by the sin of ZDN, thus found, and divide by 1800. This is the parallax correction for latitude. The mean angular diameter of the Sun is 30 minutes, and that of the Moon, 34 Minutes (according to the Romaka). Thus: (i) Parallax in latitude = sine corrected ZDN × true daily motion of the Moon ÷ 1800 (Its direc- tion is that of the ZDN). (ii) Mean angular diameter of the Sun = 30′. (iii) Mean angular diameter of the Moon = 34′. (Using (ii) and (iii) the respective true angular diameters are to be found). Under VII.1, it was explained that the parallax correction for latitude, to be used in the solar eclipse, is obtained by multiplying the horizontal parallax of the Moon relative to the Sun, by the sine of the ZDN and dividing by 120, (the max. sine). It was also shown there that the horizontal parallax itself varies inversely as the distance of the Moon from the earth, being greatest when the Moon is nearest. Hindu astronomers take it that the distance is inversely proportionate to the true daily motion, though this is only approximately correct. Therefore it is taken here that the relative parallax is proportionate to the motion, the Sun's parallax being very small compared to that of the Moon. Here, the parallax correction i.e. relative horizontal parallax × sin (corrected) ZDN ÷ 120 = Moon's daily motion × sin (corrected) ZDN ÷ 1800. From this it can be seen that according to this Siddhānta, the relative horizontal parallax is the daily motion divided by 15. Therefore the mean relative horizontal parallax = 790′.5 ÷ 15 = 52.7 minutes, as mentioned already. As for the mean angular diameters that is what the Siddhānta has found them to be, by observation or analysis of eclipses. समलिप्ता (ऽगु)विवरज्या [ऽभ्य]स्ता 'मूर्च्छना' नवहताश्च । अवनत्यायुतविश्लेषिताश्च दिक्साम्यवैलोम्ये ॥ १४ ॥ 14. Twentyone, multiplied by the sine of (Sun or Moon at new moon ~ Rāhu) and divided by nine is the latitude. This, with the parallax correction added is the parallax-corrected latitude, when both are of the same direction. When of different directions, their difference is the corrected latitude. 13. Quoted by Utpala on BS 5.18 13a. A. तज्ज्याघ्री; B1. तज्ज्याघ्नी; B2.3. तज्ज्याघ्री b. B. शनैः. A. B1.2. स्मृता नवभिः; D. स्फुटावनतिः c-d. B. त्रिशन्दानोः d. A. °स्त्रिंशान्न; B1.3. °स्त्रिशान् 14. Quoted by Utpala on BS 5.18 14a. A. लिप्ताद्वविवर; B. लिप्तिताद्व विवर; C.D. U. लिप्ताराहुविवर b. A.B1.2. न्यस्ता. D. हता च c. A. अनवद्या; B. अवनधा B. विशिल d. B. षिवाक्ष; D.U. षिता च. A1.B1. साम्ये; A2. सान्ये